Mathematical modeling and steady‐state analysis of a scheibel extraction column

The steady‐state behavior of a nine‐stage Scheibel extraction column was modeled and simulated using a back flow stagewise model. Steady‐state experiments were conducted, using the system water‐acetone‐toluene, for three phase ratios and three agitator speeds. The mathematical model was validated with the experimental concentration profiles by a single parameter fitting technique with an unconstrained optimization algorithm. Steady‐stage analysis of the experiments was performed for a further control study. The calculated steady‐state gain matrices were used for interaction analysis using different steady‐state analysis methods, e.g. Bristol numbers, Condition numbers, Morari Indexes of Integral Controllability, and Niederlinski Indexes. The results indicate that both agitator speed and phase ratio have a substantial influence on the control structure. Dynamic analysis should therefore be performed to verify the optimum control method for this process.